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A135541 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3), with a(0) = 2, a(1) = 2. 1
0, 2, 7, 12, 21, 44, 91, 180, 357, 716, 1435, 2868, 5733, 11468, 22939, 45876, 91749, 183500, 367003, 734004, 1468005, 2936012, 5872027, 11744052, 23488101, 46976204, 93952411, 187904820, 375809637, 751619276, 1503238555, 3006477108 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,2).

FORMULA

From R. J. Mathar, Feb 23 2008: (Start)

O.g.f.: -7/[5(2x-1)]-(4x+7)/[5(x^2+1)].

a(n) = [7*2^n-(-1)^[n/2]*A010712(n+1)]/5 . (End)

a(n) = (1/10)*( 7*2^(n+1) - (7 - 4*I)*I^n - (7 + 4*I)*(-I)^n ), with n>=0 and I=sqrt(-1) - Paolo P. Lava, Jun 09 2008

E.g.f.: (1/5)*( 7*cosh(2*x) + 7*sinh(2*x) - 7*cos(x) - 4*sin(x) ). - G. C. Greubel, Oct 18 2016

MATHEMATICA

LinearRecurrence[{2, -1, 2}, {0, 2, 7}, 40] (* Vincenzo Librandi, Jun 17 2012 *)

PROG

(MAGMA) I:=[0, 2, 7]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jun 17 2012

CROSSREFS

Cf. A007909, A007910, A016029, A134658.

Sequence in context: A119713 A213041 A293330 * A288656 A180804 A122264

Adjacent sequences:  A135538 A135539 A135540 * A135542 A135543 A135544

KEYWORD

nonn

AUTHOR

Paul Curtz, Feb 22 2008

EXTENSIONS

More terms from R. J. Mathar, Feb 23 2008

STATUS

approved

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Last modified December 19 06:03 EST 2018. Contains 318245 sequences. (Running on oeis4.)